Explain (in words that a non-statistics student would understand) what is meant by a ‘95% confidence interval.’
Answer: an interval of values that covers the true population value for 95% of the samples selected.
Statisticians have a phrase, “Being a statistician means never having to say you’re certain.” Do you know whether the confidence interval constructed by your sample actually contains the true population value? Why or why not?
Answer: no, because sample results vary. 95% OF THE SAMPLES WILL RESULT IN CONFIDENCE INTERVALS THAT ARE CORRECT, AND 5% WON’T. You never know whether a particular confidence interval is correct unless the truth is revealed at some future date.
A 95% confidence interval means that 95% of all possible random samples will result in an interval that contains the true population value, and 5% of them won’t. How could a confidence interval that is based on a random sample not contain the true population value?